Finite Group Databasebeta

← C2×#11924509 #14558024

Subgroups — C2×#11924509 #14558024

Order 2368.

426 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D148C211yesmaximal, characteristic, complemented
2C22×C22⋊D37C211yesmaximal, characteristic, complemented
3C22×C22⋊D37C211yesmaximal, characteristic, complemented
4C22×C4×D37C211yesmaximal, characteristic, complemented
5#11924509C218yesmaximal, direct product factor
6C2×#10596936C211yesmaximal, characteristic, complemented
7C2×#10596938C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×C37C211yesmaximal, characteristic, complemented
9C24×C37C2211yescharacteristic
10C23×D37C2211yescharacteristic
11C23×D37C2211yescharacteristic
12C22×C4×C37C2211yescharacteristic
13C22×C4×C37C2211yescharacteristic
14C2×C22⋊D37—24no—
15C2×C22⋊D37—24no—
16C2×C22⋊D37C2214yescomplemented
17C2×C22⋊D37C2214yescomplemented
18C22×Dic37C2211yescharacteristic
19C22×Dic37C2211yescharacteristic
20C2×D148—24no—
21C2×D148C2214yescomplemented
22C2×C4×D37—24no—
23C2×C4×D37C2214yescomplemented
24C22⋊C4×C37C2214yescomplemented
25#10596938C2214yescomplemented
26#10596936C2214yescomplemented
27C23×C37—22no—
28C23×C37—22no—
29C23×C37—22no—
30C23×C37C2312yes—
31C23×C37C2311yescharacteristic
32C22×D37—22no—
33C22×D37—22no—
34C22×D37—22no—
35C22×D37—22no—
36C22×D37—22no—
37C22×D37D414yescomplemented
38C22×D37C2312yes—
39C22×D37C2312yes—
40C2×C4×C37—22no—
41C2×C4×C37—22no—
42C2×C4×C37C2312yes—
43C2×C4×C37C2312yes—
44C22⋊D37—28no—
45C22⋊D37—28no—
46C2×Dic37—22no—
47C2×Dic37D414yescomplemented
48C2×Dic37C2312yes—
49C2×Dic37C2312yes—
50D148—28no—
51C4×D37—28no—
52C22×C37—22no—
53C22×C37—22no—
54C22×C37—22no—
55C22×C37—44no—
56C22×C37C2×D412yes—
57C22×C37C2×D412yes—
58C22×C37#4112yes—
59C22×C37C2411yescharacteristic
60C2×D37—28no—
61C2×D37—22no—
62C2×D37—22no—
63C2×D37—22no—
64C2×D37—22no—
65C2×D37—22no—
66C2×D37—44no—
67C2×D37C2×D414yescomplemented
68C4×C37—22no—
69C4×C37—22no—
70Dic37—22no—
71Dic37C2×D414yescomplemented
72C2×C37—42no—
73C2×C37#12114yescomplemented
74C2×C37C22×D411yescharacteristic
75C2×C37C22×D411yescharacteristic
76C2×C37C2×#4111yescharacteristic
77D37—24no—
78D37—42no—
79C2×#121—371nomaximal, Sylow
80C37C2×#12111yescharacteristic, complemented, Sylow
81C22×D4—371no—
82C22×D4—371no—
83C22×D4—371no—
84C23×C4—371no—
85#121—378no—
86C2×C4⋊C4—371no—
87C2×C22⋊C4—371no—
88C2×C22⋊C4D3711yescharacteristic, complemented
89C24—371no—
90C24—371no—
91C24C2×D3711yescharacteristic
92C2×D4—374no—
93C2×D4—374no—
94C2×D4—374no—
95C2×D4—744no—
96C2×D4—744no—
97C2×D4—744no—
98C22×C4—371no—
99C22×C4—371no—
100C22×C4—374no—
101C22×C4—744no—
102C22×C4C2×D3711yescharacteristic
103C22×C4C2×D3711yescharacteristic
104C4⋊C4—374no—
105C22⋊C4—374no—
106C22⋊C4C2×D3714yescomplemented
107C23—22no—
108C23—22no—
109C23—22no—
110C23—374no—
111C23—372no—
112C23—372no—
113C23—742no—
114C23—742no—
115C23—742no—
116C23—742no—
117C23—742no—
118C23C22×D3712yes—
119C23C22×D3711yescharacteristic
120D4—748no—
121D4—748no—
122D4—748no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—374no—
126C2×C4—372no—
127C2×C4—372no—
128C2×C4—748no—
129C2×C4—742no—
130C2×C4C22×D3712yes—
131C2×C4C22×D3712yes—
132C22—22no—
133C22—22no—
134C22—22no—
135C22—44no—
136C22—374no—
137C22—748no—
138C22—742no—
139C22—742no—
140C22—742no—
141C22—742no—
142C22—742no—
143C22—1484no—
144C22#1059696212yes—
145C22D4×D3712yes—
146C22D4×D3712yes—
147C22C23×D3711yescharacteristic
148C4—22no—
149C4—22no—
150C4—374no—
151C4—742no—
152C2—42no—
153C2—744no—
154C2—1482no—
155C2#1192450914yesdirect product factor
156C2C2×D4×D3711yescharacteristic
157C2C2×D4×D3711yescharacteristic
158C2C2×#1059696211yescharacteristic
subgroupG/H
centerC23C22×D37
commutator, cosocleC22×C37C24
FrattiniC22C23×D37
FittingC2×C22⋊C4×C37C2
socleC23×C37C23
hypercenterC2×C22⋊C4D37
hypocenterC37C2×#121
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D148C2semidirect
2. C22×C22⋊D37C2semidirect
3. C22×C22⋊D37C2semidirect
4. C22×C4×D37C2semidirect
5. #11924509C2direct (N × H)
6. C2×#10596936C2semidirect
7. C2×#10596938C2semidirect
8. C2×C22⋊C4×C37C2semidirect
16. C2×C22⋊D37C22semidirect
17. C2×C22⋊D37C22semidirect
21. C2×D148C22semidirect
23. C2×C4×D37C22semidirect
24. C22⋊C4×C37C22semidirect
25. #10596938C22semidirect
26. #10596936C22semidirect
37. C22×D37D4semidirect
47. C2×Dic37D4semidirect
67. C2×D37C2×D4semidirect
71. Dic37C2×D4semidirect
73. C2×C37#121semidirect
80. C37C2×#121semidirect
88. C2×C22⋊C4D37semidirect
106. C22⋊C4C2×D37semidirect
155. C2#11924509direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D1482
C22×C22⋊D372
C22×C4×D372
#119245092
C2×#105969362
C2×#105969382
C2×C22⋊C4×C372
C2×#12137